Spread Spectrum for Universal Compressive Sampling

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This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a suitable Krylov ...

Multiple tensor-times-matrix (Multi-TTM) is a key computation in algorithms for computing and operating with the Tucker tensor decomposition, which is frequently used in multidimensional data analysis. We establish communication lower bounds that determine ...

Spectral algorithms are some of the main tools in optimization and inference problems on graphs. Typically, the graph is encoded as a matrix and eigenvectors and eigenvalues of the matrix are then used to solve the given graph problem. Spectral algorithms ...

The increasing complexity of transformer models in artificial intelligence expands their computational costs, memory usage, and energy consumption. Hardware acceleration tackles the ensuing challenges by designing processors and accelerators tailored for t ...

For a high-dimensional problem, a randomized Gram-Schmidt (RGS) algorithm is beneficial in terms of both computational cost and numerical stability. We apply this dimension reduction technique by random sketching to Krylov subspace methods, e.g., to the ge ...

Orthogonal group synchronization is the problem of estimating n elements Z(1),& mldr;,Z(n) from the rxr orthogonal group given some relative measurements R-ij approximate to Z(i)Z(j)(-1). The least-squares formulation is nonconvex. To avoid its local minim ...

State-of-the-art Artificial Intelligence (AI) algorithms, such as graph neural networks and recommendation systems, require floating-point computation of very large matrix multiplications over sparse data. Their execution in resource-constrained scenarios, ...

Second-order Moller-Plesset perturbation theory (MP2) is the most expedient wave function-based method for considering electron correlation in quantum chemical calculations and, as such, provides a cost-effective framework to assess the effects of basis se ...

Electroencephalography (EEG) data entail a complex spatiotemporal structure that reflects ongoing organi-zation of brain activity. Characterization of the spatial patterns is an indispensable step in numerous EEG processing pipelines. We present a novel me ...

In this paper, we set the mathematical foundations of the Dynamical Low-Rank Approximation (DLRA) method for stochastic differential equations (SDEs). DLRA aims at approximating the solution as a linear combination of a small number of basis vectors with r ...

Computational chemistry aims to simulate reactions and molecular properties at the atomic scale, advancing the design of novel compounds and materials with economic, environmental, and societal implications. However, the field relies on approximate quantum ...

Single-photon 3D cameras can record the time-of-arrival of billions of photons per second with picosecond accuracy. One common approach to summarize the photon data stream is to build a per-pixel timestamp histogram, resulting in a 3D histogram tensor that ...

Sylvester matrix equations are ubiquitous in scientific computing. However, few solution techniques exist for their generalized multiterm version, as they now arise in an increasingly large number of applications. In this work, we consider algebraic parame ...

Modern data management systems aim to provide both cutting-edge functionality and hardware efficiency. With the advent of AI-driven data processing and the post-Moore Law era, traditional memory-bound scale-up data management operations face scalability ch ...

The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated re -assemblage of finite element matrices for nonlinear PDEs is frequently pointed ...

This work is concerned with approximating matrix functions for banded matrices, hierarchically semiseparable matrices, and related structures. We develop a new divide-and-conquer method based on (rational) Krylov subspace methods for performing low-rank up ...

The Transfer Matrix formalism is ubiquitous when it comes to study wave propagation in various stratified media, applications ranging from Seismology to Quantum Mechanics. A relation between variables at two points in two different layers can be establishe ...

Data-driven schemes that associate molecular and crystal structures with their microscopic properties share the need for a concise, effective description of the arrangement of their atomic constituents. Many types of models rely on descriptions of atom-cen ...

Machine learning frameworks based on correlations of interatomic positions begin with a discretized description of the density of other atoms in the neighborhood of each atom in the system. Symmetry considerations support the use of spherical harmonics to ...

The Schur decomposition of a square matrix A is an important intermediate step of state-of-the-art numerical algorithms for addressing eigenvalue problems, matrix functions, and matrix equations. This work is concerned with the following task: Compute a (m ...

Spread Spectrum for Universal Compressive Sampling

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SPEEDING UP KRYLOV SUBSPACE METHODS FOR COMPUTING f(A)b VIA RANDOMIZATION

COMMUNICATION LOWER BOUNDS AND OPTIMAL ALGORITHMS FOR MULTIPLE TENSOR-TIMES-MATRIX COMPUTATION

The Power of Two Matrices in Spectral Algorithms for Community Recovery

Accelerator-driven Data Arrangement to Minimize Transformers Run-time on Multi-core Architectures

Randomized flexible GMRES with deflated restarting

BENIGN LANDSCAPES OF LOW-DIMENSIONAL RELAXATIONS FOR ORTHOGONAL SYNCHRONIZATION ON GENERAL GRAPHS

A 16-bit Floating-Point Near-SRAM Architecture for Low-power Sparse Matrix-Vector Multiplication

Plane Waves Versus Correlation-Consistent Basis Sets: A Comparison of MP2 Non-Covalent Interaction Energies in the Complete Basis Set Limit

Spectral representation of EEG data using learned graphs with application to motor imagery decoding

Dynamical Low-Rank Approximation for Stochastic Differential Equations

Advancing Computational Chemistry with Stochastic and Artificial Intelligence Approaches

Learned Compressive Representations for Single-Photon 3D Imaging

Preconditioning techniques for generalized Sylvester matrix equations

Post-Moore's Law Fusion: High-Bandwidth Memory, Accelerators, and Native Half-Precision Processing for CPU-Local Analytics

On the fast assemblage of finite element matrices with application to nonlinear heat transfer problems

DIVIDE-AND-CONQUER METHODS FOR FUNCTIONS OF MATRICES WITH BANDED OR HIERARCHICAL LOW-RANK STRUCTURE\ast

Harmonic decomposition of the trace of 1D transfer matrices in layered media

Unified theory of atom-centered representations and message-passing machine-learning schemes

A smooth basis for atomistic machine learning

Iterative refinement of Schur decompositions